Banach Journal of Mathematical Analysis

Duality for increasing convex functionals with countably many marginal constraints

Daniel Bartl, Patrick Cheridito, Michael Kupper, and Ludovic Tangpi

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Abstract

In this work we derive a convex dual representation for increasing convex functionals on a space of real-valued Borel measurable functions defined on a countable product of metric spaces. Our main assumption is that the functionals fulfill marginal constraints satisfying a certain tightness condition. In the special case where the marginal constraints are given by expectations or maxima of expectations, we obtain linear and sublinear versions of Kantorovich’s transport duality and the recently discovered martingale transport duality on products of countably many metric spaces.

Article information

Source
Banach J. Math. Anal., Volume 11, Number 1 (2017), 72-89.

Dates
Received: 17 October 2015
Accepted: 18 February 2016
First available in Project Euclid: 10 November 2016

Permanent link to this document
https://projecteuclid.org/euclid.bjma/1478746987

Digital Object Identifier
doi:10.1215/17358787-3750133

Mathematical Reviews number (MathSciNet)
MR3571145

Zentralblatt MATH identifier
06667688

Subjects
Primary: 47H07: Monotone and positive operators on ordered Banach spaces or other ordered topological vector spaces
Secondary: 46G12: Measures and integration on abstract linear spaces [See also 28C20, 46T12] 91G20: Derivative securities

Keywords
representation results increasing convex functionals transport problem Kantorovich duality model-independent finance

Citation

Bartl, Daniel; Cheridito, Patrick; Kupper, Michael; Tangpi, Ludovic. Duality for increasing convex functionals with countably many marginal constraints. Banach J. Math. Anal. 11 (2017), no. 1, 72--89. doi:10.1215/17358787-3750133. https://projecteuclid.org/euclid.bjma/1478746987


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